Господин Экзамен
log(16-2*x,4)-2*log(9,4) если x=-3/2
Решение
Вы ввели
[src]
log(16 - 2*x)
------------- - 2*log(47/5)
log(4)
$$\frac{\log{\left(- 2 x + 16 \right)}}{\log{\left(4 \right)}} - 2 \log{\left(\frac{47}{5} \right)}$$
log(16 - 2*x)/log(4) - 2*log(47/5)
Общее упрощение
[src]
/ -log(16) \
log\2*47/5 *(8 - x)/
---------------------------
log(4)
$$\frac{\log{\left(\frac{2 \cdot \left(- x + 8\right)}{\left(\frac{47}{5}\right)^{\log{\left(16 \right)}}} \right)}}{\log{\left(4 \right)}}$$
log(2*(8 - x)/(47/5)^log(16))/log(4)
Подстановка условия
[src]
log(16 - 2*x)/log(4) - 2*log(47/5) при x = -3/2
подставляем
log(16 - 2*x)
------------- - 2*log(47/5)
log(4)
$$\frac{\log{\left(- 2 x + 16 \right)}}{\log{\left(4 \right)}} - 2 \log{\left(\frac{47}{5} \right)}$$
/ -log(16) \
log\2*47/5 *(8 - x)/
---------------------------
log(4)
$$\frac{\log{\left(\frac{2 \cdot \left(- x + 8\right)}{\left(\frac{47}{5}\right)^{\log{\left(16 \right)}}} \right)}}{\log{\left(4 \right)}}$$
переменные
x = -3/2
$$x = - \frac{3}{2}$$
/ -log(16) \
log\2*47/5 *(8 - (-3/2))/
--------------------------------
log(4)
$$\frac{\log{\left(\frac{2 \cdot \left(- (-3/2) + 8\right)}{\left(\frac{47}{5}\right)^{\log{\left(16 \right)}}} \right)}}{\log{\left(4 \right)}}$$
/ -log(16) \
log\2*47/5 *(8 - -3/2)/
------------------------------
log(4)
$$\frac{\log{\left(\frac{2 \cdot \left(\left(-1\right) \left(- \frac{3}{2}\right) + 8\right)}{\left(\frac{47}{5}\right)^{\log{\left(16 \right)}}} \right)}}{\log{\left(4 \right)}}$$
/ -log(16)\
log\19*47/5 /
--------------------
log(4)
$$\frac{\log{\left(\frac{19}{\left(\frac{47}{5}\right)^{\log{\left(16 \right)}}} \right)}}{\log{\left(4 \right)}}$$
log(19/(47/5)^log(16))/log(4)
Комбинаторика
[src]
-4*log(2)*log(47) + 4*log(2)*log(5) + log(16 - 2*x)
---------------------------------------------------
2*log(2)
$$\frac{\log{\left(- 2 x + 16 \right)} - 4 \log{\left(2 \right)} \log{\left(47 \right)} + 4 \log{\left(2 \right)} \log{\left(5 \right)}}{2 \log{\left(2 \right)}}$$
(-4*log(2)*log(47) + 4*log(2)*log(5) + log(16 - 2*x))/(2*log(2))
Численный ответ
[src]
-4.48141937855192 + 0.721347520444482*log(16 - 2*x)
-4.48141937855192 + 0.721347520444482*log(16 - 2*x)
Объединение рациональных выражений
[src]
-2*log(4)*log(47/5) + log(2*(8 - x))
------------------------------------
log(4)
$$\frac{\log{\left(2 \cdot \left(- x + 8\right) \right)} - 2 \log{\left(4 \right)} \log{\left(\frac{47}{5} \right)}}{\log{\left(4 \right)}}$$
(-2*log(4)*log(47/5) + log(2*(8 - x)))/log(4)
Рациональный знаменатель
[src]
-2*log(4)*log(47/5) + log(16 - 2*x)
-----------------------------------
log(4)
$$\frac{\log{\left(- 2 x + 16 \right)} - 2 \log{\left(4 \right)} \log{\left(\frac{47}{5} \right)}}{\log{\left(4 \right)}}$$
(-2*log(4)*log(47/5) + log(16 - 2*x))/log(4)
Общий знаменатель
[src]
1 log(8 - x) - - 2*log(47) + 2*log(5) + ---------- 2 2*log(2)
$$\frac{\log{\left(- x + 8 \right)}}{2 \log{\left(2 \right)}} - 2 \log{\left(47 \right)} + \frac{1}{2} + 2 \log{\left(5 \right)}$$
1/2 - 2*log(47) + 2*log(5) + log(8 - x)/(2*log(2))
Собрать выражение
[src]
-log(16)*log(47/5) + log(16 - 2*x)
----------------------------------
log(4)
$$\frac{\log{\left(- 2 x + 16 \right)} - \log{\left(\frac{47}{5} \right)} \log{\left(16 \right)}}{\log{\left(4 \right)}}$$
(-log(16)*log(47/5) + log(16 - 2*x))/log(4)